consider the function (x)=3−6x2 f ( x ) = 3 − 6 x 2 on the interval [−6,4] [ − 6 , 4 ] . Find the average or mean slope of the function on this interval, i.e. (4)−(−6)4−(−6) f ( 4 ) − f ( − 6 ) 4 − ( − 6 ) Answer: By the Mean Value Theorem, we know there exists a c c in the open interval (−6,4) ( − 6 , 4 ) such that ′(c) f ′ ( c ) is equal to this mean slope. For this problem, there is only one c c that works. c= c = Note: You can earn partial credit on this problem

The relation accepts reflexive, symmetry, and transitive.

Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.

If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.

And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.

Given r is a relation on the set of all nonnegative integers R(a,b)

Reflexive - YES. A given number a will always have the same remainder when divided by 5.

Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.

Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.

Therefore the relation accepts reflexive, symmetry, and transitive.

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Answer:

....try t out

The answer is 40

Answer:

Quotient=42

Step-by-step explanation:

Answer:

2x - y = -8

Step-by-step explanation:

Answer:

Hi! To find x (the missing angles of the triangles), remember that the angles in a triangle add up to 180 degrees. This means that for each triangle, you can add the two angles given, then subtract that number from 180 to find x. I'll use Triangle 1 as an example:

81 + 84 = 165

180 - 165 = 15

So for Triangle 1, x is equal to 15.

To classify each triangle by angles, remember that an acute triangle has three angles that each measure less than 90 degrees, a right triangle is a triangle with one 90 degree angle, and an obtuse triangle is a triangle with one angle that is greater than 90 degrees. To classify each triangle by sides, remember that scalene triangles have three sides of unequal length, isosceles triangles have two sides of equal length, and equilateral triangles have three sides of equal length.

Keeping all this in mind, here are your answers:

Triangle 1 - 15 acute scalene

Triangle 2 - 120 obtuse scalene

Triangle 3 - 41 right scalene

Triangle 4 - 104 obtuse isosceles

Triangle 5 - 25 right scalene

Triangle 6 - 64 acute scalene

Triangle 7 - 72 acute scalene

Triangle 8 - 32 obtuse scalene

Triangle 9 - 40 right scalene

I hope this helps you! Have a great day. - Mani :)

Answer: Third proportion is 21/5.

Step-by-step explanation:

Let the proportion be x

so,

3:5:x:7

so

3:5 = x:7

or, 3/5 = x/7

or, 21 = 5x

or, x = 21/5

Answer:

h(6) = 9

Step-by-step explanation:

h(x) = 2x – 3,

Let x = 6

h(6) = 2*6 -3

       = 12 -3

       = 9

Answer:

h(6) = 9

Step-by-step explanation:

To evaluate h(6), substitute x = 6 into h(x) , that is

h(6) = 2(6) - 3 = 12 - 3 = 9

Answer:

2

Step-by-step explanation:

Answer:

7 4/5 or 7.8

Step-by-step explanation:

S1: Convert mixed number to an improper fraction

36/5 - (-3/5)

S2: Add the fractions

36/5 + 3/5

Answer 39/5

Simplify:

7 4/5 or 7.8

Answer:

5. 36 square inches

2. Answer is B.

3. 189 cm^2

Step-by-step explanation:

5. 6 + 6 + 6 + 8 + 10 = 36

3. 51 + 102 + 36 = 189

Answer:

p=24

Step-by-step explanation:

p=2(7)+2(5)

p=14+10

pp=24

Answer:

XM = 1 unit

Step-by-step explanation:

It is given that, M is the midpoint in the segment.

Midpoint bisects the lines such that,

XM = MY

Put XM = x+2 and MY = 2x+3

x+2=2x+3

Taking like terms together,

x-2x=3-2

-x=1

x = -1

Put x = -1 in XM = x+2

(-1) + 2 = 1 = XM

So, the value of XM is 1 unit.

The area bounded by the curves y = √(x) and y = x^2 is approximately 0.23 square units.

The area bounded by the curves y = √(x) and y = x^2 can be found by integrating both functions within the given range. To determine the points of intersection, we set the two equations equal to each other:

√(x) = x^2

Rearranging the equation, we get:

x^2 - √(x) = 0

Solving this equation will yield two points of intersection, x = 0 and x ≈ 0.59. To find the area, we integrate the difference between the two curves within this range:

A = ∫[0, 0.59] (x^2 - √(x)) dx

Evaluating this integral gives us the approximate area of 0.23 square units.

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The test statistic of null and alternative hypotheses for a test is 0.811.

69 of the 142 persons that were randomly chosen from a sample are found to meet the condition we are testing.

The sample proportion phat = 69 ÷ 142 = 0.489

n = 69

p = 0.54

the following are your test's null and alternate hypotheses:

\(H_0\) : p = 0.54

\(H_a\) : p < 0.54,

test statistic,

z = (phat - p) ÷ √(p × (1 - p) ÷ n)

z = (0.489 - 0.54) ÷ √((0.79 × 0.21) ÷ 42) = 0.811

A test statistic is a figure obtained from a statistical analysis. It explains how distant the observational values seem to be from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

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In order to get 97% confidence level, with confidence interval of

+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples

A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.

Accordingly, the Necessary Sample Size is calculated as follows:

Necessary Sample Size = \((Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}\)

Given:-

Substituting in the given formula we get

Necessary Sample Size =

= ((2.17)² x 0.5(0.5)) / (0.01)²

= (4.7089x 0.25) / .0001

= 1.177225 / 0.0001

= 11,772.25

Hence in order to get 97% confidence level, with confidence interval of

+/- 1%,  and standard deviation of 0.5 our sample size should be 11,772

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Answer:

584,615

Step-by-step explanation:

its rounded by the whole number

Belmont will produce 584,615 metric tons of CO₂ after 6 years, growing at the rate of 10% every year, currently emitting 330,000 metric tons of CO₂.

The value of most things is not constant in this world. If we observe correctly, the value of some of the things rises, while others fall. If there is a rise, we call it growth.

Growth can be determined by the formula,

V = V₀(1+r)ⁿ, where V is the final value, V₀ is the initial value, r is the rate and n is the time.

In the question, we are given that Belmont is a growing industrial town. Every year, the level of CO2 emissions from the town increases by 10%.

We are asked that if the town produced 330,000 metric tons of CO2 this year, how much will be produced 6 years in the future.

As we see that the amount of CO₂ emission is growing, to find the amount of CO₂ emitted in the 6th year, we use the growth formula,

V = V₀(1+r)ⁿ, where V is the final value, V₀ is initial value, r is rate, and n is the time period.

Here, V₀ = 330,000 metric tons, r = 10%, n = 6 years.

∴ V = 330,000(1 + 10%)⁶

or, V = 330,000(1.1)⁶ = 330,000*1.771561 = 548615.13

or, V = 548615 metric tons (rounded to nearest whole number).

∴ Belmont will produce 584,615 metric tons of CO₂ after 6 years, growing at the rate of 10% every year, currently emitting 330,000 metric tons of CO₂.

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The value of the numerical expression \(\sqrt{ 288 \times \left (\frac{2}{3}\right) \times \left (\frac{1}{3}\right)}\) will be 8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The statement is given as "the square root of the product of 288 and two-thirds and one-third​".

Then the expression is written as,

\(\rightarrow \sqrt{ 288 \times \left (\dfrac{2}{3}\right) \times \left (\dfrac{1}{3}\right)}\)

Simplify the expression, then we have

⇒ √(576 / 9)

⇒ 24 / 3

⇒ 8

The value of the numerical expression \(\sqrt{ 288 \times \left (\frac{2}{3}\right) \times \left (\frac{1}{3}\right)}\) will be 8.

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Answer:

\(\sqrt{12}\) units

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the other leg, then

x² + 2² = 4²

x² + 4 = 16 ( subtract 4 from both sides )

x² = 12 ( take the square root of both sides )

x = \(\sqrt{12}\) units

which can be simplified to 2\(\sqrt{3}\) units , if required.

So the elevation of the clock is approximately 39.1 meters above the ground.

Trigonometry is a branch of mathematics that deals with the study of triangles, particularly the relationships between the sides and angles of triangles. It is used to calculate the relationships between the sides and angles of triangles in order to solve real-world problems related to areas such as architecture, engineering, physics, and astronomy. Trigonometric functions, such as sine, cosine, and tangent, are used to calculate these relationships.

Here,

We can use the tangent function to find the elevation of the clock:

tan(15°) = opposite / adjacent

where the opposite side is the elevation we want to find and the adjacent side is the horizontal distance from Penny's yard to the clock:

tan(15°) = x / 140

Multiplying both sides by 140, we get:

x = 140 tan(15°)

Using a calculator, we find that:

x ≈ 39.1 meters

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Answer:

Answer D

Step-by-step explanation:

Solve for b:

\(\frac{1}{2}b \geq 4\)

Divide both sides by a half

\(b\geq 8\)

We see that its a greater than or equal too sign, which means the number line has to be facing to the right with a closed circle. Therefore, D is our answer.

If T is a linear transformation then the standard matrix of T is \(\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right]\).

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The transformation is given as - T : IR² → IR²

Take the (x,y) values as x(1,0) and y(0,1)

(x,y) = x(1,0) + y(0,1)

Apply the transformation -

T(x,y) = T[x(1,0) + y(0,1)]

Since T is a linear map then -

T(x,y) = x T((1,0)) + y T((0,1))

Now, substitute the values -

T(x,y) = x Te1 + y Te2

T(x,y) = x [e1 - 19e2] + y [e2]

T(x,y) = x e1 + e2(-19x + y)

Resubstitute the values back -

T(x,y) = x (1,0) + (0,1)(-19x + y)

T(x,y) = (x , -19x+y)

For T : IR² → IR²

T(x,y) = (ax+by , cx+dy)

Then A = \(\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\)

So, now the matrix A is -

A = \(\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right]\)

Therefore, the matrix is  \(\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right]\).

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Answer:

\(l(\overline {AB})\approx9.22\: units\)

Step-by-step explanation:

a) The point on the curve where the tangent is horizontal is at t = 0.

b) The points where the tangent is vertical are at t₁ = -5 and t₂ = 5.

To find the points on the curve where the tangent is horizontal, we need to find the values of t that satisfy dy/dt = 0.

a.) Differentiating y = 3(t² - 75) with respect to t, we get:

dy/dt = 6t

Setting dy/dt = 0, we have:

6t = 0

t = 0

Therefore, when t = 0, the tangent is horizontal.

b.) To find the points where the tangent is vertical, we need to find the values of t that satisfy dx/dt = 0.

Differentiating x = t(t² - 75) with respect to t, we get:

dx/dt = 3t² - 75

Setting dx/dt = 0, we have:

3t² - 75 = 0

t² = 25

t = ±5

Therefore, the points where the tangent is vertical are when t = -5 and t = 5, with t₁ = -5 and t₂ = 5.

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The question is -

Consider the curve given by the parametric equations

x = t (t²-75) , y = 3 (t²-75)

a.) Determine the point on the curve where the tangent is horizontal.

t=

b.) Determine the points t_1,t_2 where the tangent is vertical and t_1 < t_2.

t_1=

t_2=

7(x+2)

Let's find the common term in this expression to factor it out. it is 7.

Factoring is the opposite of distributing.

If we distribute, we will get the original expression.

Next:

45-27k

Here, the common term is 9:

9(5-3k)

12ab+7b - the common term is b:

b(12a+7)

y^2-9y.

Here the common term is y:

y(y-9)

8r-32r² the common term here is 8r:

8r(1-4r)

16gh+28gh: the Common Term is 4gh:

4gh(4+7)

21w²-77wx The common term is 7w:

7w(3w-11x)

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\(*VirtuosoTeen*\)

\(^R^O^S^A^L^I^N^D\) \(^C^O^R^D^E^L^I^A\)

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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The equation of the line is y = 3x, and the graph is a straight line.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given are points we need to find the equation of a line that passes through these lines,

We know that, the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by;

y-y₁ = y₂-y₁ / (x₂-x₁) (x-x₁)

Here, (x₁, y₁) and (x₂, y₂) are (3,9) and (2,6);

Therefore,

y-9 = 6-9 / 2-3 (x-3)

y-9 = 3(x-3)

y-9 = 3x-9

y = 3x

Hence, the equation of the line is y = 3x

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The graph of the functions, from narrowest to widest, are ordered as follows:

A. m(x) = −10x², p(x) = 8x², r(x) = 0.6x²

A quadratic function is defined as follows:

y = ax².

The absolute value of the leading coefficient a determines the width of the function, and the higher the absolute value of the coefficient, the narrower the graph of the function is.

Hence the graphs are ordered as follows:

m(x) = −10x², p(x) = 8x², r(x) = 0.6x².

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Answer:

B and D

Step-by-step explanation:

Hopefully this helps :D

Answer:

y = -2x - 1

Step-by-step explanation:

If you already know the slope. Just find out the y-intercept. Plug the coordinates into the equation.

y = mx + b

y = -2x + b

1 = -2(1) + b

1 = -2 + b

-1 = b

The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.

The total number of balls that that where present at the battling practice by Alexis = 15.

The number of balls that hit into the outfield = 8

The number of balls that hit outside the outfield = 15-8= 7

The percentage (x) of the balls that are outside the outfield;

X = 8/15 × 100/1

x ×15 = 8 × 100

15/8 = X/100.

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Answer:

9. The 5 bags for $25 is a better deal

10. You would need $16.72

Step-by-step explanation:

9. Divide 25/5=5 and 42/7=6

The 5 bags for $25 is a better deal because it's the smallest answer.

10. Divide $12.54/6=$2.09 per book

Multiply $2.09*8=$16.72 for 8 books

Answer:

9. The 5 bags for $25.00 is the best offer.

10. 8 books is $16.72.

Step-by-step explanation:

9. Because you have to find out how much each bag costs so you divide the total cost by the ammount of bags. When you do this you get $5 dollars a bag for the 5 bags and $6 dollars a bag for the 7 bags.

10. You need to find out how much each book cost so you divide the amount of money by 6 and you get $2.09. Then you multiple 8 by 2.09 and you get 1672 but then you have to move the decimal to the left two times and you end up with $16.72.